One day, the mayor of the town called all the masters into the town square for a meeting. The mayor said, "I have some sad news to report. I have been informed that there is AT LEAST ONE apprentice who is a thief and has been stealing from his master. I have verified it myself." Surprisingly, the masters were not surprised. Each master knew which of the other apprentices were thieves, but did not suspect his own.
"Now," the mayor continued, "to avoid name calling, each master is responsible for reporting his own apprentice if he discovers that his apprentice is a thief." The masters agreed that this was a good plan. "On the first day of the upcoming year, we will meet here again in the town square at noon. If any master knows that his apprentice is a thief, he should declare so. If no one comes forth, everyone can go home, and we will meet again each day until the thieves have been exposed."
Assuming that the mayor's words are true, on which day is each of the thieves exposed? Hint: the number of masters and apprentices does not matter.